Recession flow analysis is a hydrological technique used in many studies (e.g. Brutsaert and Nieber, 1977; Troch et al., 1993; Parlange et al., 2001; Rupp and Selker, 2006; Kirchner, 2009) based on widely available streamflow records. As it has been commonly applied, recession flow analysis is a graphical analysis in which recession flow (dQ/dt) is related to discharge (Q) in log–log space and fit with a straight line (Figure 1). While such a functional form of the storage–discharge relationship does not need to be assumed a priori (Kirchner, 2009), it can be a useful assumption such that the parameters of the assumed function can be interpreted as reflecting catchment-scale hydrologic parameters. Recession flows primarily depend on the physiographic characteristics of a catchment, which are related to the geomorphology of the landscape and stream network and the configuration of the riparian aquifers and near-surface soils (Brutsaert, 2005).
In northern regions, permafrost distribution, permafrost thickness and thickness of the active layer contribute to the physiographic characteristics of a catchment and may be considered primary controls on hydrologic response (Hinzman et al., 2005). In many arctic and sub-arctic regions, the depth to the permafrost largely determines the pathways of water flow through the landscape (Kane et al., 1981). Ice layers at the interface of the organic and mineral soils are a main cause of lateral run-off with much research emphasising their role in water storage and restriction of transmittance properties (Santeford, 1979; Slaughter and Kane, 1979; Hinzman et al., 1993; McNamara et al., 1997, 1998). The terrestrial freshwater cycle in the arctic and sub-arctic is intimately connected with the presence of permafrost (White et al., 2007; Woo et al., 2008). In addition to influencing the hydrological response of the landscape, the location and distribution of these pathways influence the carbon and other biogeochemical cycling in northern latitude catchments (MacLean et al., 1999; McNamara et al., 2008). Permafrost change and thawing has also been identified as a key proxy for changes in climate by the International Polar Year framework (International Council for Science, 2004). Direct observations of permafrost change, however, are difficult to perform at scales larger than the local scale, and there is a need for indirect detection methods of permafrost change and its effects on larger scales.
Recent work by Lyon et al. (2009) outlines a theoretical connection between recession flow analysis and changes in permafrost position at the catchment scale. This work differs from previous recession analysis in northern systems (Carey and Woo, 2001; Yamazaki et al., 2006) in that Lyon et al. (2009) related long-term trends (>10 years) in recession intercept values to changes in catchment-scale depth to permafrost that influences storage–discharge dynamics, while the other studies looked at recession characteristics within a season. Lyon et al. (2009) were able to use recession flow analysis to obtain an estimate of permafrost thawing rate in a single, sub-arctic Swedish catchment, underlain by discontinuous permafrost. The goal of the present study is to perform a wider test of the ability of recession flow analysis to reflect thawing of permafrost at the catchment scale. This is done by applying the methodology outlined in Lyon et al. (2009) to the well-studied Yukon river basin (YRB) covering large portions of Alaska, USA and parts of Canada. We hypothesise that there should be shift in the trend of the recession flow intercept (following the methodology in Lyon et al. (2009)) corresponding to permafrost warming and thawing caused by a regional shift to warmer air temperatures in 1976/1977 (Trenberth, 1990; Osterkamp and Romanovsky, 1999; Neal et al., 2002; Osterkamp, 2007).
2. Permafrost conditions in the YRB
Recently, Walvoord and Striegl (2007) examined long-term streamflow records in 21 catchments of the YRB. They observed highly significant (p < 0.05) increases in winter flow for 16 of these 21 catchments. These increases occurred without strong evidence of any precipitation increases, suggesting that the winter flow increases were due to increases in the groundwater contribution to streamflow. Walvoord and Striegl (2007) concluded that these increases were caused predominately by climate warming and permafrost thawing, enhancing infiltration and supporting deeper groundwater flow paths.
Permafrost is present to a large extent in the YRB with great variation in extent and thickness (Brabets et al., 2000). The western region of the YRB is generally underlain by moderately thick to thin permafrost, and the northern central region is generally underlain by continuous permafrost (Figure 2). The central region is underlain by discontinuous permafrost and numerous isolated permafrost masses, while the southwestern region is considered to contain more sporadic masses of permafrost. In total, the more discontinuous and sporadic permafrost regions account for about 60% of the total area of the YRB. The depth to permafrost varies across the YRB from relatively shallow regions where the maximum thaw depth of the active layer reaches about 30–80 cm deep (Osterkamp, 2005) to regions where the permafrost layer is much deeper (greater than several meters deep) (Brabets et al., 2000).
Hinzman et al. (2005) give a thorough overview of climate change studies in Alaska (and other arctic regions), documenting increases in air temperatures and permafrost warming. In general, air temperatures have warmed from about the end of the 1800s through about 1940 (Hamilton, 1965; Osterkamp, 2007). Cooler temperatures continued until a more-or-less statewide step-like shift in temperatures of about 1 to 2 °C occurred in 1976/1977 (Osterkamp and Romanovsky, 1999; Osterkamp, 2007). Warming peaked in the mid-1980s, after which the temperatures slightly cooled through the early 1990s. More recently, warmer temperatures are observed, with the temperatures from 2000 to 2006 being consistently warm and about the same as in the period around 1980 (Osterkamp, 2007). These specific warming trends are consistent with the general warming of the Arctic reported by Serreze et al. (2000) for the last 30 years.
Borehole temperature measurements, thermokarst observations, basal thawing measurements and modelling investigations indicate that permafrost warming in Alaska is coincident with the regional warming of air temperatures that began in 1976/1977 (Osterkamp, 2007). During the last quarter of the 20th century, several studies highlight a warming of permafrost surface temperatures in northern Alaska and along the north–south transect of the Alaskan permafrost observatories that stretch from the northern Alaskan coastline (∼70°N latitude) at Prudhoe Bay to about the southern Alaskan coastline (∼62°N latitude) at Gulkana (Osterkamp and Romanovsky, 1999; Clow and Urban, 2002; Romanovsky et al., 2003; Osterkamp, 2005, 2007). In response to the permafrost warming, Osterkamp and Romanovsky (1999) report that thawing of the permafrost has been occurring from the top downward in both tundra and forest sites at a rate of about 0.1 m/year.
3. Recession flow analysis theory and methodology
In this study, we make use of the same 21 catchments presented in Walvoord and Striegl (2007) and apply the methodology of recession flow analysis for detecting catchment-scale permafrost thawing that was proposed by Lyon et al. (2009). These 21 catchments are monitored by streamflow gauging stations operated by either the United States Geological Survey (USGS) or Environment Canada. All 21 gauges have publicly available records accessible via the internet at http://waterdata.usgs.gov/nwis and http://www.wsc.ec.gc.ca/hydat/H2O for the sites maintained by the USGS and Environment Canada, respectively. We use the daily streamflow measurements over the entire record period for each catchment in this study. This is approximately the same data set analyzed by Walvoord and Striegl (2007). One notable exception to this is the stream gauge on Porcupine river near Fort Yukon, Alaska (site 15). For this site, the length of the daily streamflow record available from the USGS website (15 years of data) is shorter than that reported in Walvoord and Striegl (2007) (36 years of data).
Physical considerations based on hydraulic groundwater theory suggest that the total groundwater storage in a catchment can be approximated as a power function of base flow rate at the catchment outlet (Brutsaert, 2008):
where dQ/dt is the temporal change of the flow rate at the outlet during flow recession and the constants a and b give the intercept and slope of a plot of dQ/dt versus flow Q in log–log space, respectively. For several well-known solutions of the Boussinesq equation, a can be related to aquifer properties and b may assume certain constant values depending on time since the onset of drainage, bedrock slope and reservoir properties (Brutsaert, 2005). In practice, recession flow analysis consists of relating the rate of decline of the hydrograph, which is assumed to result solely from groundwater storage (i.e. periods of record when there is no forcing due to rainfall or excessive snowmelt), to observed hydrograph outflow.
For the long-time solution of the fundamental harmonic linearised solution to the Boussinesq equation (Brutsaert, 2005), the constant a (i.e. intercept) and b values can be related to aquifer properties such that:
where k is the hydraulic conductivity, p is an empirical weighting constant ranging roughly between 0.3 and 0.1, or perhaps even smaller as the water table further declines in the range of lowest flows (Brutsaert, 2008), D is the depth of the aquifer, L is the total length of the channel network, ne is the drainable porosity and A is the catchment area. Lyon et al. (2009) demonstrated that it is possible to infer changes in the effective depth to permafrost at the catchment scale using Equation (3) based on long-term daily streamflow observations. Inherent to such an inference is the assumption that there is no change in the geomorphic characteristics (L and A) and no (or relatively small) change in the hydrologic characteristics (k and ne) in Equation (3). Geomorphic characteristics are not likely to change over this period of observation as they evolve at much longer timescales and tend to reach an equilibrium state (Brutsaert, 2008). Since hydraulic conductivity tends to decay with depth in most arctic systems (Quinton et al., 2000, 2008), the depth-averaged hydraulic conductivity under thawing conditions can be assumed to be relatively minimal compared to the effect of changes in depth on the storage–discharge relationship (Lyon et al., 2009).
Long-term changes in the intercept, a, of a recession flow analysis can thus be interpreted as changes in the effective depth of the aquifer, D, (Brutsaert, 2008) which is closely related to the position and depth extent of permafrost. This considers permafrost thawing as a long-term process, in addition to the seasonal fluctuations of the active layer. Yamazaki et al. (2006) looked at recession characteristics and attributed monthly variations to seasonal changes in active layer thickness. McNamara et al. (1998) showed that recession properties of streams in northern Alaska change due to seasonal thawing as the depth of the active layer increases. While these seasonal variations in recession properties occur at a different temporal scale, they clearly demonstrate that recession is indeed reliant on the depth D.
We applied the above theory using a methodology similar to that outlined by Lyon et al. (2009) to investigate if permafrost thawing at the catchment scale is reflected as changes in recession flow properties in the YRB. Streamflow records for each of the catchments in the YRB were divided into 5-year periods starting from 1950 (e.g. 1950–1959, 1960–1964). This starting year coincides with the year in which 5 of the 21 catchments had year-round daily observations of streamflow. For each 5-year period, we only considered streamflow occurring in ‘late-summer’ periods, August and September, for the further recession flow analysis. This was done to isolate periods of recession flows resulting primarily from groundwater storage and minimise the possible influence of excessive snowmelt at lower elevations. As perennial snowfields cover about 1% and glaciers cover an additional 1% of the total YRB (Brabets et al., 2000), it is unavoidable to include periods when snow is present in some of the catchments even during these short late-summer periods; similar conditions existed for the catchment considered in the work of Lyon et al. (2009). In addition to the small fraction of snow covered area in YRB, we assume that direct sublimation, evaporation of pond water and root water uptake will minimise the influence of melt water on the recession flow analysis.
Periods of rising streamflow and 3 days following each hydrograph peak were removed from the hydrograph records because these periods are likely influenced by direct rainfall. Focusing on the late-summer periods of each streamflow record implies also that a perched groundwater system should have existed above the permafrost, which could contribute shallow subsurface flow to the channel network. For each 5-year period of streamflow, filtered as described above, Equation (1) was fit through all points in a plot of dQ/dt versusQ, similar to the approach presented by Parlange et al. (2001) and Lyon et al. (2009) using a non-linear least squares fitting procedure shown to be adequate for this type of analysis (Lyon et al., 2009). This procedure also allowed us to avoid the difficulty of defining a lower envelop of the cloud of points in the dQ/dt versusQ plot. Equation (1) was fit to the resulting dQ/dt versusQ plot by using Equation (2) of constant b and solving only for the intercept, a, of each 5-year period.
Intercepts from the recession flow analysis performed for each 5-year period vary over the available period of record for each catchment in the YRB (Figure 3). The intercept values shown for each catchment in Figure 3 have been normalised by the average intercept of all 5-year periods of that catchment, enabling direct comparison between the different catchments. In Figure 3, each point represents the normalised intercept from the recession flow analysis of the 5-year period following the year indicated. For example, a point plotted at 1960 is the normalised intercept from the recession flow analysis of streamflow data for 1960–1969.
Linear regression is used to investigate the intercept trends for each catchment. Figure 3 shows the fitted linear trends for three time periods: (1) the entire period of record, (2) the period from the record start through to 1975–1979 and (3) the period fit from 1975 to 1979 through to the end of record. The break-point for the latter two trend fits was selected to correspond approximately to the regional temperature shift occurring in Alaska in the mid-1970s (1976/1977). This shift marks a significant change in air temperatures in the region and has been identified as the starting point for the shift in permafrost surface temperatures (Osterkamp, 2007). Using two separate linear trends (i.e. one before and one after the temperature shift) allows for a significant (p < 0.05) improvement of the overall fit to the intercept values, compared to using one regression trend through the whole series comparing all catchments where there are enough data.
For each catchment in the YRB, we can compare the slopes of the linear trends fit to the recession intercepts for the period before (Figure 4(a); beginning to 1975) and after (Figure 4(b); 1975 to end) the 1976/1977 regional temperature shift. A positive slope indicates an increasing and a negative slope a decreasing intercept trend over the period. Sites 11, 16 and 18 did not have enough data to create at least three points for fitting a trend for the period before the 1975 break-point. Additionally, sites 15 and 20 did not have enough data to create at least three points for fitting a trend for the period after the 1975 break-point. These catchments are, thus, excluded from the following analysis. There is a significant (p < 0.05) increase in regression line slopes from the period before and that after the 1976/1977 temperature shift. Looking across all the catchments where there are enough data to fit trends, the median of the regression line slopes is significantly (p < 0.05) positive after the 1976/1977 temperature shift, while it is negative and not significantly (p < 0.05) different from zero before this shift (Figure 4). Of the catchments with enough data, 33% (6 of 18) had positive slopes in the period prior to the 1976/1977 temperature shift, while 68% (13 of 19) had positive slopes in the period after the temperature shift. Comparing the pre- and post-temperature shift slopes, all but 1 of the 12 catchments with negative slopes prior to the temperature shift have increased slopes after the temperature shift, with 6 of these catchment slopes becoming positive after the shift.
Catchment-scale permafrost conditions influence the slope of the linear trend fit to the periods before and after the regional 1976/1977 temperature shift in the YRB. Assuming constant catchment-scale effective geomorphologic and hydrologic parameters, there is a physical interpretation of the significant changing (from negative to positive) slopes of the recession flow intercept trends after the 1976/1977 temperature shift as an increasing catchment-scale effective depth to permafrost (Lyon et al., 2009). This is also seen in the significant increase of the remaining negative slopes after this temperature shift reflecting permafrost changes in response to the regional warming.
This physical interpretation of the trends in the recession flow intercepts for the YRB is supported by observed permafrost thawing and increases in thermokarst terrain (marking subsidence of the surface due to thawing of ice-rich permafrost) at several sites in interior Alaska (Hinzman et al., 2005). For example, sites 17 and 18, which have the highest slopes in the linear trend fits from 1975 through the end of record (Figure 4(b)), drain catchments that are classified to a large extent as being generally underlain by discontinuous permafrost. The discontinuous permafrost is sensitive to changes in air temperature and is likely to exhibit evidence of large-scale permafrost thawing before regions that are underlain by more continuous permafrost. In interior Alaska, discontinuous permafrost is warming and thawing, and extensive areas of thermokarst terrain are developing as a result of climatic change (Osterkamp and Romanovsky, 1999; Osterkamp 2005). Such thawing has also been directly observed in the southern regions of the YRB. Osterkamp (2005) reported on a tundra site near Healy that has been thawing at the top since the late 1980s at about 10 cm/year. Osterkamp and Romanovsky (1999) have reported the same value for a forested site on the University of Alaska Fairbanks campus. Both of these observation sites are located in the vicinity of the gauging sites 17 and 18.
For the sites with data available for the last 5-year period (2000–2004) considered in this study, several show a considerable intercept increase, in particular, for this last period relative to previous periods (e.g. sites 1 and 3 in Figure 3). This could be a reflection of the first 6 years of the 21st century being consistently warmer than the mid-1990s (Osterkamp, 2007). We can also compare the change in intercept after the mid-1970s (1975–1979) temperature shift for the sites that Walvoord and Striegl (2007) found to have a highly significant (p < 0.05) annual average increase in groundwater. For these sites, there is a clear positive correlation between the relative change in recession flow intercept (as percentage increase from 1975 to 1979) and the relative increase in annual groundwater flow (R2 = 0.58, Figure 5). Walvoord and Striegl (2007) proposed that the groundwater flow increases were caused predominately by climate warming and permafrost thawing, enhancing infiltration and supporting deeper groundwater flow paths. Similar studies have used changes in groundwater flows (estimated using winter flows) to infer long-term permafrost thawing in the northwest territories of Canada (St. Jacques and Sauchyn, 2009) and Eurasia (Smith et al., 2007). The results from the present recession flow analysis support this interpretation (specifically in the YRB) on the basis of hydraulic theory.
Permafrost thawing involves many interactions between various physical, biological and anthropogenic factors. As a result, the spatial patterns of permafrost thawing rates at the catchment scale are likely to change over time and space. Add to this that permafrost may thaw from both its top and its bottom, and it is obvious that permafrost thawing is a complex, variable process. As such, a few local observations of permafrost and permafrost thawing may not be able to capture accurately the overall catchment-scale changes. Recession flow analysis provides a methodology for reflecting catchment-scale permafrost changes over time. While the trend in the recession slopes can be attributed primarily to increased depth to permafrost (e.g. Lyon et al., 2009), they might also be related to changes in spatial extent of permafrost. This relationship between recession flow analysis and spatial extent of permafrost warrants further investigation. The recession flow analysis reflects changes in subsurface storage at the catchment scale. Kirchner (2009) demonstrated that if a catchment can be represented by a single storage element in which discharge is a function of storage alone, the form of this storage–discharge function can be estimated from analysis of streamflow fluctuations. The main strength of the recession flow analysis is its ability to capture the integral effect of the process complexity present in a catchment's subsurface on the catchment's run-off recession characteristics with a much simpler set of equations than if all the complexity were modelled in detail.
The recession flow analysis methodology that was outlined by Lyon et al. (2009) for detecting and estimating the rate of permafrost thawing has been applied to daily streamflow records in the YRB. It is demonstrated that the regional warming that started in 1976/1977 produced a significant shift (p < 0.05) in recession intercepts. Based on the theory outlined in Lyon et al. (2009), this can be attributed to thawing permafrost. Coincident to this, direct observations of thawing across central Alaska have been made corresponding to the same temperature shift. In addition, there is good agreement between the catchments exhibiting the largest increase in recession flow intercept (a proxy for effective depth to permafrost) in the present study and the catchments having the observed groundwater flow increases in the study by Walvoord and Striegl (2007). These results demonstrate that the method developed by Lyon et al. (2009) is applicable to catchments that are underlain by a variety of permafrost conditions. The strength of this method is that it requires only daily observations of streamflow to reflect catchment-scale permafrost thawing. Such data are widely available over long-time records for many arctic and sub-arctic regions, on catchment scales that represent much larger measurement support scales than the local scales of direct permafrost observation. Recession flow analysis should thus be a useful technique for mapping large-scale regions of thawing permafrost and provide a framework to compare thawing rates between different regions.
Funding came from the Swedish Research Council (VR) and the Bert Bolin Centre for Climate Research, which is supported by a Linnaeus grant from VR and The Swedish Research Council Formas. Two reviewers are gratefully thanked for their comments.